Macedonia on Monday accused non-governmental aid organizations of inciting migrants to provoke incidents from the Greek side of the border where they have been stranded for nearly two months.
On Sunday, a large group of migrants had attempted to break through a border fence near the camp at Idomeni, to which Macedonian riot police responded with force and tear gas.
Greece meanwhile blasted its neighbour for what it said was excessive use of force. "With such treatment of refugees, Macedonia can have no place in either NATO, or the European Union," Greek President Prokopis Pavlopoulos said.
Athens has already been blocking Skopje on its path to EU membership because of their row over the name Macedonia, which Greece claims for its northern province.
Greek Civic Protection Minister Nikos Toskas warned that frustration among migrants stranded at the border might lead to their radicalization. "What you're seeing today are the jihadists of tomorrow," he told Skai TV.
As a result of Sunday's incident, close to 300 migrants at the Idomeni camp required medical assistance, mostly for respiratory problems and contusions, while, according to a Macedonian Interior Ministry statement, more than 20 police officers were hurt.
In a statement issued on Monday, the Ministry said that around 3,000 migrants took part in the onslaught on the border. Two groups of several hundred crossed the border, but were swiftly returned, it said.
Some of the migrants had leaflets on them suggesting that once they broke through the Greek-Macedonia border, they would be allowed to continue toward EU member states in Western Europe, the Ministry said, accusing unnamed NGOs of distributing them.
Apart from large international organizations, including UN agencies and big names, such as Doctors Without Borders, there are many smaller groups helping out at camp Idomeni, with some handing out food and others providing clothes. Some also offer free legal advice.
The Ministry denied Greek reports saying that Macedonian officers fired rubber bullets and stun grenades at the crowd.
The camp at Idomeni was initially set up as a temporary measure for up to 2,000 people at the height of the migration crisis, when thousands of people moved along the Balkan route every day, travelling from Turkey across Greece, Macedonia, Serbia, Croatia and Slovenia.
Now around 12,000 have been stranded there since February, when Macedonia and other countries on the route sealed their borders to migrants, including refugees from war zones in Syria and Iraq.
The refugees can now only hope to get asylum in the EU through a mechanism agreed with Turkey. Despite assurances from both Macedonian and Greek authorities that the border will remain closed to them, thousands at Idomeni have refused to leave.
"The commission will continue to send the message that the people in Idomeni should be relocated or housed in reception facilities in Greece and should not attempt a dangerous and irregular onward journey," European Commission spokeswoman Mina Andreeva told journalists in Brussels on Monday.
"All authorities and NGOs concerned should provide correct information to the migrants in Idomeni in this regard in order to avoid further incidents," she added.
While Athens remains reluctant to press the migrants into relocating to official camps and centres, local Mayor Christos Goudenoudis said Idomeni should be cleared by the end of April. "The situation is on razor's edge," he told Skai.
Aid organizations have been warning for months that conditions in the overcrowded official facility and the makeshift camp surrounding it are unfit for humans.
Meanwhile, the influx of migrants arriving in Greece from Turkey drastically dropped in the wake of the EU-Turkey deal.
Only 18 were reported as having made the sea journey from Turkey over a 24-hour period, the office in Athens responsible for the migration crisis said Monday, compared with 162 the day before and thousands a day in the latter half of 2015.